Computers are everywhere. It's gotten so that it's hard to find an employee who isn't using one in the course of his or her day - whether he be CEO or salesman, engineer or machinist. Everywhere you look, you find the familiar neutral-colored boxes and bright glowing screens. And despite the gear industry's traditional reluctance to embrace new technology, more and moe of what you find on those screens are gears.

Romax Technology, the gearbox, bearing
and driveline engineering specialist, has launched a new design software package that will increase speed, quality, creativity and innovation when designing gearboxes and drivelines. Called Concept, the new product delivers on the Romax vision of streamlining the end-to-end, planning-to-manufacture process with open, easy to use software solutions. It has been developed in close collaboration with engineers in the largest ground vehicle, wind energy and industrial
equipment companies around the globe.

Gear engineers have long recognized the importance of considering system factors when analyzing a single pair of gears in mesh. These factors include important considerations
such as load sharing in multi-mesh geartrains and bearing clearances, in addition to the effects of flexible components such as housings, gear blanks, shafts and carriers for planetary geartrains. However, in recent years, transmission systems have become increasingly complex—with higher numbers of gears and components—while the quality requirements and expectations in terms of durability, gear whine, rattle and efficiency
have increased accordingly.

Gear design has long been a "black art." The gear shop's modern alchemists often have to solve problems with a combination of knowledge, experience and luck. In many cases, trial and error are the only effective way to design gears. While years of experience have produced standard gearsets that work well for most situations, today's requirements for quieter, more accurate and more durable gears often force manufacturers to look for alternative designs.

The complete and accurate solution t the contact problem of three-dimensional gears has been, for the past several decades, one of the more sought after, albeit elusive goals in the engineering community. Even the arrival on the scene in the mid-seventies of finite element techniques failed to produce the solution to any but the most simple gear contact problems.

Light-weight construction and consideration of available resources result in gearbox designs with high load capacity and power density. At the same time, expectations for gear reliability are high. Additionally, there is a diversity of planetary gears for different applications.

Many CAD (Computer Aided Design) systems have been developed and implemented to produce a superior quality design and to increase the design productivity in the gear industry. In general, it is true that a major portion of design tasks can be performed by CAD systems currently available. However, they can only address the computational aspects of gear design that typically require decision-making as well. In most industrial gear design practices, the initial design is the critical task that significantly effects the final results. However, the decisions about estimating or changing gear size parameters must be made by a gear design expert.

"Design for manufacturability" (DFM) is a well-established practice, essential to realizing the successful transformation of concepts into mass-produced gears and motion control
devices. And yet, all too often issues that could have been avoided are
identified very late in the process that
impact production costs and schedules.
This suggests that key DFM principles
are often underutilized in practice and
are not applied consistently - or to the
degree necessary - to avoid these negative results.

There is a great need for future powertrains in automotive and industrial applications to improve upon their efficiency and power density while reducing their dynamic vibration and noise initiation. It is accepted that planetary gear transmissions have several advantages in comparison to conventional transmissions, such as a high power density due to the power division using several planet gears. This paper presents planetary gear transmissions, optimized in terms of
efficiency, weight and volume.

By increasing the number of gears and the transmission-ratio spread, the engine will run with better fuel
efficiency and without loss of driving
dynamics. Transmission efficiency
itself can be improved by: using fuelefficient transmission oil; optimizing the lubrication systems and pumps; improving shifting strategies and optimizing gearings; and optimizing bearings and seals/gaskets.

This paper will provide examples of stress levels from conventional root design using a hob and stress levels using an optimized root design that is now possible with PM manufacturing. The paper will also investigate how PM can reduce stresses in the root from transient loads generated by abusive driving.

A gear design optimization approach applied to reduce tooth contact temperature and noise excitation of a high-speed spur gear pair running without lubricant. Optimum gear design search was done using the Run Many Cases software program. Thirty-one of over 480,000 possible gear designs were considered, based on low contact temperature and low transmission error. The best gear design was selected considering its manufacturability.

Flank breakage is common in a number of cylindrical and bevel gear applications. This paper introduces a relevant, physically based calculation method to evaluate flank breakage risk vs. pitting
risk. Verification of this new method through testing is demonstrably shown.

Planetary gear transmissions are compact, high-power speed reducers that use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane transmission, the planet gear has no size of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary transmission with a fixed size, gear ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives, which point to an optimal planetary reduction ratio in the neighborhood of four to five.

A gear shaper cutter is actually a gear with relieved cutting edges and increased addendum for providing clearance in the root of the gear being cut. The maximum outside diameter of such a cutter is limited to the diameter at which the teeth become pointed. The minimum diameter occurs when the outside diameter of the cutter and the base circle are the same. Those theoretical extremes, coupled with the side clearance, which is normally 2 degrees for coarse pitch cutters an d1.5 degrees for cutters approximately 24-pitch and finer, will determine the theoretical face width of a cutter.

Plastic gears are serious alternatives to traditional metal gears in a wide variety of applications. The use of plastic gears has expanded from low-power, precision motion transmission into more demanding power transmission applications. As designers push the limits of acceptable plastic gear applications, more is learned about the behavior of plastics in gearing and how to take advantage of their unique characteristics.

Gears are manufactured with thin rims for several reasons. Steel gears are manufactured with thin rims and webs where low weight is important. Nonmetallic gears, manufactured by injection molding, are designed with thin rims as part of the general design rule to maintain uniform thickness to ensure even post-mold cooling. When a thin-rimmed gear fails, the fracture is thought the root of the gear, as shown in Fig. 1a, rather than the usual fillet failure shown in Fig. 1b.

simplified equations for backlash and roll test center distance are derived. Unknown errors in measured tooth thickness are investigate. Master gear design is outlined, and an alternative to the master gear method is described. Defects in the test radius method are enumerated. Procedures for calculating backlash and for preventing significant errors in measurement are presented.

This is Part II of a two-part series on the basics of gear hobbing. Part I discussed selection of the correct type of hobbing operation, the design features of hobs and hob accuracy. This part will cover sharpening errors and finish hob design considerations.

When designing hardened and ground spur gears to operate with minimum noise, what are the parameters to be considered? should tip and/or root relief be applied to both wheel and pinion or only to one member? When pinions are enlarged and he wheel reduced, should tip relief be applied? What are the effects on strength, wear and noise? For given ratios with enlarged pinions and reduced wheels, how can the gear set sized be checked or adjusted to ensure that the best combination has been achieved?

Powder metallurgy (P/M) is a precision metal forming technology for the manufacture of parts to net or near-net shape, and it is particularly well-suited to the production of gears. Spur, bevel and helical gears all may be made by made by powder metallurgy processing.

This article discusses the relationships among the fillet stress on a thin rim planet gear, the radial clearance between the gear rim and the gear shaft, the tooth load, the rim thickness, the radius of curvature of the center line of the rim, the face width and the module.

The primary objective in designing reliable gear drives is to avoid failure. Avoiding failure is just as important for the manufacturer and designer as it is for the end user. Many aspects should be considered in order to maximize the potential reliability and performance of installed gearing.

It has been documented that epicyclic gear stages provide high load capacity and compactness to gear drives. This paper will focus on analysis and design of epicyclic gear arrangements that provide extremely high gear ratios. Indeed, a special, two-stage planetary arrangement may utilize a gear ratio of over one hundred thousand to one. This paper presents an analysis of such uncommon gear drive arrangements and defines their major parameters, limitations, and gear ratio maximization approaches. It also demonstrates numerical examples, existing designs, and potential applications.

When designing a gear set, engineers usually want the teeth of the gear (Ng) and the pinion (Np) in a "hunting" mesh. Such a mesh or combination is defined as one in which the pinion and the gear do not have any common divisor by a prime number. If a mesh is "hunting," then the pinion must make Np x Ng revolutions before the same pinion tooth meshes with the same gear space. It is often easy to determine if a mesh is hunting by first determining if both the pinion and the gear teeth are divisible by 2,3,5,7,etc. (prime numbers). However, in this age of computerization, how does one program the computer to check for hunting teeth? A simple algorithm is shown below.

A major source of helicopter cabin noise (which has been measured at over 100 decibels sound pressure level) is the gearbox. Reduction of this noise is a NASA and U.S. Army goal. A requirement for the Army/NASA Advanced Rotorcraft Transmission project was a 10 dB noise reduction compared to current designs.

Gearbox performance, reliability, total cost of ownership (energy cost), overall impact on the environment, and anticipation of additional future regulations are top-of-mind issues in the industry. Optimization of the bearing set can significantly improve gearbox performance.

You're already a veteran of the computer revolution. Only you and your controller know how much money you've spent and only your spouse knows how many sleepless nights you've had in the last ten years trying to carve out a place in the brave new world of computerized gear manufacturing. PC's, CNCs, CAD, CAM, DNC, SPC, CMM: You've got a whole bowl of alphabet soup out there on the shop floor. Overall these machines have lived up to their promises. Production time is down, quality is up. You have fewer scrapped parts and better, more efficient machine usage.

Information is the name of the game in the 90s. We need more of it; we need it faster; and we need it in infinitely manipulatable and user-friendly form. In many cases, getting it that way is still something of a Holy Grail, somewhere off on the distant horizon. But thanks to computer technology, bit by byte, we're getting there.

Arrow Gear Company of Downers Grove, IL, has implemented a computer system that fully integrates exchange between all of its computer applications. The ELIMS (Electronic Linkage of Information Management Systems) project has increased manufacturing productivity and reduced lead times.

It used to be that a shop with hustle and plenty of big, fast machines could thrive using a manual system. But no more. Today's economic environment requires more and more in the way of topnotch service and quick turnaround - which frequently means a completely integrated shop floor control system.

Most gear cutting shops have shelves full of expensive tooling used in the past for cutting gears which are no longer in production. It is anticipated that these cutters will be used again in the future. While this may take place if the cutters are "standard," and the gears to be cut are "standard," most of the design work done today involves high pressure angle gears for strength, or designs for high contact ratio to reduce noise. The re-use of a cutter under these conditions requires a tedious mathematical analysis, which is no problem if a computer with the right software is available. This article describes a computerized graphical display which provides a quick analysis of the potential for the re-use of shaving cutters stored in a computer file.

In this issue of Gear Technology, we are focusing on using computers to their greatest advantage in gear design and manufacturing. In a sense, that's old news. It's a cliche to suggest that computers make our work life easier and more productive. No company that wishes to remain competitive in today's global manufacturing environment can afford to be without computers in all their manifestations. We need them in the office; we need them next to our desks in place of drafting boards; we need them on the shop floor.

Designing and manufacturing gears requires the skills of a mathematician, the knowledge of an engineer and the experience of a precision machinist. For good measure, you might even include the are of a magician, because the formulas and calculations involved in gear manufacturing are so obscure and the processes so little known that only members of an elite cadre of professionals can perform them.

So there is little chance that they need the same software to assist with their work. Gone are the days when companies wrote their own code and process engineers thumbed the same tattered reference book.

A programmable algorithm is developed to separate out the effect of eccentricity (radial runout) from elemental gear inspection date, namely, profile and lead data. This algorithm can be coded in gear inspection software to detect the existence, the magnitude and the orientation of the eccentricity without making a separate runout check. A real example shows this algorithm produces good results.

The aim of this article is to show a practical procedure for designing optimum helical gears. The optimization procedure is adapted to technical limitations, and it is focused on real-world cases. To emphasize the applicability of the procedure presented here, the most common optimization techniques are described. Afterwards, a description of some of the functions to be optimized is given, limiting parameters and restrictions are defined, and, finally, a graphic method is described.

The availability of technical software has grown rapidly in the last few years because of the proliferation of personal computers. It is rare to find an organization doing technical work that does not have some type of computer. For gear designers and manufacturers, proper use of the computer can mean the difference between meeting the competition or falling behind in today's business world. The right answers the first time are essential if cost-effective design and fabrication are to be realized. The computer is capable of optimizing a design by methods that are too laborious to undertake using hard calculations. As speeds continue to climb and more power per pound is required from gear systems, it no longer is possible to design "on the safe side" by using larger service factors. At high rotational speeds a larger gear set may well have less capacity because of dynamic effects. The gear engineer of today must consider the entire gear box or even the entire rotating system as his or her domain.

A computational fluid dynamics (CFD) method is adapted, validated and applied to spinning gear systems with emphasis on predicting windage losses.
Several spur gears and a disc are studied. The CFD simulations return good agreement with measured windage power loss.

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ration under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque and power. Significant parameters in the design are the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near-optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

The first edition of the international calculation method for micropitting—ISO TR 15144–1:2010—was just published
last December. It is the first and only official, international calculation method established for dealing with
micropitting. Years ago, AGMA published a method for the calculation of oil film thickness containing some comments
about micropitting, and the German FVA published a calculation method based on intensive research results. The FVA and the AGMA methods are close to the ISO TR, but the calculation of micropitting safety factors is new.

Profile corrections on gears are a commonly used method to reduce transmission error, contact shock, and scoring risk. There are different types of profile corrections. It is a known fact that the type of profile correction used will have a strong influence on the resulting transmission error. The degree of this influence may be determined by calculating tooth loading during mesh. The current method for this calculation is very complicated and time consuming; however,
a new approach has been developed that could reduce the calculation time.

Tooth contact under load is an important verification of the real contact conditions of a gear pair and an
important add-on to the strength calculation according to standards such
as ISO, AGMA or DIN. The contact analysis simulates the meshing of the
two flanks over the complete meshing
cycle and is therefore able to consider
individual modifications on the flank
at each meshing position.

In this paper, the potential for geometrical cutting simulations—via penetration calculation to analyze and predict tool wear as well as to prolong tool life—is shown by means of gear finish hobbing.
Typical profile angle deviations
that occur with increasing
tool wear are discussed. Finally,
an approach is presented here to
attain improved profile accuracy
over the whole tool life of the finishing
hob.

Gear manufacturers are moving into an era that will see changes in both engineering practices and industry
standards as new end-products evolve. Within the traditional automotive
industry, carbon emission reduction
legislation will drive the need for higher levels of efficiency and growth in electric and hybrid vehicles.
Meanwhile, the fast growing market of wind turbines is already opening up a whole new area of potential for gearbox manufacturers, but this industry is one that will demand reliability, high levels of engineering excellence and precision manufacturing.

The face load factor is one of the most important items for a gear strength calculation. Current standards propose formulae for face load factor, but they are not always appropriate. AGMA 927 proposes a simpler and quicker algorithm that doesn't require a contact analysis calculation. This paper explains how this algorithm can be applied for gear rating procedures.

Questions: I have heard the terms "safety factor," "service factor," and "application factor" used in discussing gear design. what are these factors an dhow do they differ from one another? Why are they important?

This paper describes the research and development of the first production gearbox with asymmetric tooth profiles for the TV7-117S turboprop engine. The paper also presents numerical design data related to development of this gearbox.

LMS International helped a Fiat subsidiary develop a new, dynamic vibro-acoustic prediction method to reduce design time and engineering costs through accurate prediction of gear noise in the design phase.

Above all, a gear is not just a mechanical transmission, but is developed to a system fulfilling multiple demands, such as clutch integration, selectable output speeds, and controls of highest electronic standards. This paper shows the basics for high-speed gear design and a selection of numerous applications in detailed design and operational needs.

In this paper, an accurate FEM analysis has been done of the “true” stress at tooth root of spur gears in the function of the gear geometry. The obtained results confirm the importance of these differences.

A series of bench-top experiments was conducted to determine the effects of metallic debris being dragged through meshing gear teeth. A test rig that is typically used to conduct contact fatigue experiments was used for these tests. Several sizes of drill material,
shim stock and pieces of gear teeth were introduced and then driven through the meshing region. The level of torque required to drive the “chip” through the gear mesh was measured. From the data gathered, chip size sufficient to jam the mechanism can be determined.

One of the most effective methods in solving the edge loading problem due to excess misalignment and deflection in aerospace actuation gearing is to localize tooth-bearing contact by crowning the teeth. Irrespective of the applied load, if the misalignment and/or deflection are large enough to cause the contact area to reduce to zero, the stress becomes large enough to cause failure. The edge loading could cause the teeth to break or pit, but too much crowning may also cause the teeth to pit due to concentrated loading. In this paper, a proposed method to localize the contact bearing area and calculate the contact stress with crowning is presented and demonstrated on some real-life examples
in aerospace actuation systems.

This paper presents a unique approach and methodology to define the limits of selection for gear parameters. The
area within those limits is called the “area of existence of involute gears” (Ref. 1). This paper presents the definition and construction of areas of existence of both external and internal gears. The isograms of the constant operating pressure
angles, contact ratios and the maximum mesh efficiency (minimum sliding) isograms, as well as the interference
isograms and other parameters are defined. An area of existence allows the location of gear pairs with certain characteristics. Its practical purpose is to define the gear pair parameters that satisfy specific performance requirements before
detailed design and calculations. An area of existence of gears with asymmetric teeth is also considered.

An offshore jack-up drilling rig is a barge upon which a drilling platform is placed. The barge has legs that can be lowered to the sea floor to support the rig. Then the barge can be “jacked up” out of the water, providing a stable work platform from which to drill for oil and gas. Jack-up drilling rigs were first introduced in the late 1950s. Rack-and- pinion-type jack-up units were introduced soon after that and have dominated the industry ever since.

If a gear system is run continuously for long periods of time—or if the starting loads are very low and within the normal operating spectrum—the effect of the start-up conditions may often be insignificant in the determination of the life of the gear system. Conversely, if the starting load is significantly higher than any of the normal operating conditions,
and the gear system is started and stopped frequently, the start-up load may, depending on its magnitude and frequency, actually be the overriding, limiting design condition.

In the field of large power transmission gear units for heavy machine industry, the following two development trends have
been highly influential: use of case hardened gears and a branching of the power flow through two or more ways.

Excess lubricant supply in gearing contributes to power loss due to churning as well as the requirements of the lubrication system itself. Normally, a much larger amount of oil than required is used for cooling because so much of it is thrown away by centrifugal force. To lower the amount of lubricant required and
reduce those losses, it is necessary to discover the ideal location of the supplying nozzle.

The method of cutting teeth on a cylindrical gear by the hobbing process has been in existence since the late 1800s. Advances have been made over the years in both the machines and the cutting tools used in the process. This paper will examine hob tool life and the many variables that affect it. The paper will cover the state-of-the-art cutting tool materials and coatings, hob tool design
characteristics, process speeds and feeds, hob shifting strategies, wear characteristics, etc. The paper will also discuss the use of a common denominator method for evaluating hob tool life in terms of meters (or inches) per hob tooth as an alternative to tool life expressed in parts per sharpening.

With the right selection of nonstandard center distance and tool shifting, it may be possible to use standard tools to improve the gear set capacity with a considerable reduction in cost when compared to the use of special tools.

In most transmission systems, one of the main power loss sources is the loaded gear mesh. In this article, the influences of gear geometry parameters on gear efficiency, load capacity, and excitation are shown.

Calculation of gear tooth flexibility is of interest for at least two reasons: (a) It controls, at least in part, the vibratory properties of a transmission system hence, fatigue resistance and noise: (b) it controls load sharing in multiple tooth contact.

The use of plastic gearing is increasing steadily in new products.
This is due in part to the availability of recent design data. Fatigue
stress of plastic gears as a function of diametral pitch, pressure angle,
pitch line velocity, lubrication and life cycles are described based
on test information. Design procedures for plastic gears are presented.

The development of a new gear strength computer program based upon the finite element method, provides a better way to calculate stresses in bevel and hypoid gear teeth. The program incorporates tooth surface geometry and axle deflection data to establish a direct relationship between fillet bending stress, subsurface shear stress,
and applied gear torque. Using existing software links to other gear analysis programs allows the gear engineer to evaluate the strength performance of existing and new gear designs as a function of tooth contact pattern shape, position and axle deflection characteristics. This approach provides a better understanding of how gears react under load to subtle changes in the appearance of the no load tooth
contact pattern.

High speed gearing, operating with low viscosity lubricants, is prone to a failure mode called scoring. In contrast
to the classic failure modes, pitting and breakage, which generally take time to develop, scoring occurs early in the
operation of a gear set and can be the limiting factor in the gear's power capability.

In today’s manufacturing environment, shorter and more efficient product
development has become the norm. It is therefore important to consider every
detail of the development process, with a particular emphasis on design. For
green machining of gears, the most productive and important process is hobbing. In order to analyze process design for this paper, a manufacturing simulation was developed capable of calculating chip geometries and process forces based on different models. As an important tool for manufacturing technology engineers, an economic feasibility analysis is implemented as well. The aim of this paper is to show how an efficient process design—as well as an efficient process—can be designed.

Advancements in machining and assembly techniques of thermoplastic gearing along with new design data has lead to increased useage of polymeric materials. information on state of the art methods in fabrication of plastic gearing is presented and the importance
of a proper backlash allowance at installation is discussed. Under controlled conditions, cast nylon gears show 8-14 dBA. lower noise level than three other gear materials tested.

In this paper a new method for the introduction of optimal modifications into gear tooth surfaces—based on the
optimal corrections of the profile and diameter of the head cutter, and optimal variation of machine tool settings for pinion and gear finishing—is presented. The goal of these tooth modifications is the achievement of a more favorable
load distribution and reduced transmission error. The method is applied to face milled and face hobbed hypoid gears.

A gear can be defined as a toothed wheel which, when meshed with another toothed wheel with similar configuration, will transmit rotation from one shaft to another. Depending upon the type and accuracy of motion desired, the gears and the profiles of the gear teeth can be of almost any form.

Engineering design requires many different types of gears and splines. Although these components are rather expensive, subject to direct wear, and difficult to replace, transmissions with gears and splines are required for two very simple reasons:
1) Motors have an unfavorable (disadvantageous) relation of torque to number of revolutions.
2)Power is usually required to be transmitted along a shaft.

A universal gear is one generated by a common rack on a cylindrical, conical, or planar surface, and whose teeth can be oriented parallel or skewed, centered, or offset, with respect to its axes. Mating gear axes can be parallel or crossed, non-intersecting or intersecting, skewed or parallel, and can have any angular orientation (See Fig.1) The taper gear is a universal gear. It provides unique geometric properties and a range of applications unmatched by any other motion transmission element. (See Fig.2) The taper gear can be produced by any rack-type tool generator or hobbing machine which has a means of tilting the cutter or work axis and/or coordinating simultaneous traverse and infeed motions.

Cutter Sharpening
Cutter sharpening is very important both during manufacturing and subsequently in resharpening after dulling. Not only does this process affect cutter "over cutting edge" quality and the quality of the part cut, but it can also affect the manner in which chip flow takes place on the cutter face if the surface finished is too rough or rippled.

The paper describes a procedure for the design of internal gear pairs, which is a generalized form of the long and short addendum system. The procedure includes checks for interference, tip interference, undercutting, tip interference during cutting, and rubbing during cutting.

Gear shaping is one of the most popular production choices in gear manufacturing. While the gear shaping process is really the most versatile of all the gear manufacturing methods and can cut a wide variety of gears, certain types of gears can only be cut by this process. These are gears closely adjacent to shoulders; gears adjacent to other gears, such as on countershafts; internal gears, either open or blind ended; crown or face gears; herringbone gears of the solid configuration of with a small center groove; rack; parts with filled-in spaces or teeth, such as are used in some clutches.

In many gear transmissions, a tooth load on one flank is significantly higher and is applied for longer periods of time than for the opposite one; an asymmetric tooth shape reflects
this functional difference. This paper describes an approach that rationalizes the degree of asymmetry (or asymmetry factor K) selection to meet a variety of operating conditions and requirements for custom gear drives.

This is a three-part article explaining the principles of gear lubrication. It reviews current knowledge of the field of gear tribology and is intended for both gear designers and gear operators. Part 1 classifies gear tooth failures into five modes and explains the factors that a gear designer and operator must consider to avoid gear failures. It defines the nomenclature and gives a list of references for those interested in further research. It also contains an in-depth discussion of the gear tooth failure modes that are influenced by lubrication and gives methods for preventing gear tooth failures.

What follows is Part 2 of a three-part article covering the principles of gear lubrication. Part 2 gives an equation for calculating the lubricant film thickness, which determines whether the gears operate in the boundary, elastohydrodynamic, or full-film lubrication regime. An equation for Blok's flash temperature, which is used for predicting the risk of scuffing, is also given.

To mechanical engineers, the strength of gear teeth is a question of constant recurrence, and although the problem to be solved is quite elementary in character, probably no other question could be raised upon which such a diversity of opinion exists, and in support of which such an array of rules and authorities might be quoted. In 1879, Mr. John H. Cooper, the author of a well-known work on "Belting," made an examination of the subject and found there were then in existence about forty-eight well-established rules for horsepower and working strength, sanctioned by some twenty-four authorities, and differing from each other in extreme causes of 500%. Since then, a number of new rules have been added, but as no rules have been given which take account of the actual tooth forms in common use, and as no attempt has been made to include in any formula the working stress on the material so that the engineer may see at once upon what assumption a given result is based, I trust I may be pardoned for suggesting that a further investigation is necessary or desirable.

Today's high technology hobs are visible different from their predecessors. Gear hobs have taken on a different appearance and function with present day technology and tool and material development. This article shows the newer products being offered today and the reasons for investigating their potential for use in today's modern gear hobbers, where cost reduction and higher productivity are wanted.

The design of any gearing system is a difficult, multifaceted process. When the system includes bevel gearing, the process is further complicated by the complex nature of the bevel gears themselves. In most cases, the design is based on an evaluation of the ratio required for the gear set, the overall envelope geometry, and the calculation of bending and contact stresses for the gear set to determine its load capacity. There are, however, a great many other parameters which must be addressed if the resultant gear system is to be truly optimum.
A considerable body of data related to the optimal design of bevel gears has been developed by the aerospace gear design community in general and by the helicopter community in particular. This article provides a summary of just a few design guidelines based on these data in an effort to provide some guidance in the design of bevel gearing so that maximum capacity may be obtained. The following factors, which may not normally be considered in the usual design practice, are presented and discussed in outline form:
Integrated gear/shaft/bearing systems
Effects of rim thickness on gear tooth stresses
Resonant response

The finished gear engineer, the man who is prepared for all emergencies, must first of all know the basic design principles.
Next he must be well versed in all sorts of calculations which come under the heading of "involute trigonometry."

This article describes a method of obtaining gear tooth profiles from the geometry of the rack (or hob) that is used to generate the gear. This method works for arbitrary rack geometries, including the case when only a numerical description of the rack is available. Examples of a simple rack, rack with protuberances and a hob with root chamfer are described. The application of this technique to the generation of boundary element meshes for gear tooth strength calculation and the generation of finite element models for the frictional contact analysis of gear pairs is also described.

In our last issue, the labels on the drawings illustrating "Involutometry" by Harlan Van Gerpan and C. Kent Reece were inadvertently omitted. For your convenience we have reproduced the corrected illustrations here. We regret any inconvenience this may have caused our readers.

Traditionally, a worm or a multi-stage gear box has been used when a large speed ratio is required. However, such boxes will become obsolete as size and efficiency become increasingly important considerations for a modern transmission. The single-enveloped worm gear has a maximum speed ratio of only 40 to 60. Its efficiency is only 30 to 60 per cent. The necessity of using bronze for the worm gear and grinding nitoalloy steel for the worm drives up material and manufacturing costs.

The use of dimensionless factors to describe gear tooth geometry seems to have a strong appeal to gear engineers. The stress factors I and J, for instance, are well established in AGMA literature. The use of the rack shift coefficient "x" to describe nonstandard gear proportions is common in Europe, but is not as commonly used in the United States. When it is encountered in the European literature or in the operating manuals for imported machine tools, it can be a source of confusion to the American engineer.

When specifying a complete gear design, the novice designer is confronted with an overwhelming and frequently confusing group of options which must be specified. This array of specifications range from the rather vague to the very specific.

When a gear set is to be designed for a new application, the minimum size gears with the required capacity are desired. These gears must be capable of meeting the power, speed, ratio, life, and reliability requirements.

Selection of the number of teeth for each gear in a gear train such that the output to input angular velocity ratio is a specified value is a problem considered by relatively few published works on gear design.

In designing involute gear teeth, it is essential that the fundamental
properties of the involute curve be clearly understood. A review of "the Fundamental Laws of the Involute Curve"
found in last issue will help in this respect. It has previously been shown that the involute curve has its origin at the base circle. Its length, however, may be anything from zero at the origin or starting point on to infinity. The problem, therefore, in designing gear teeth, is to select that portion of the involute, which will best meet all requirements.

The geometry factor, which is a fundamental part of the AGMA strength rating of gears, is currently computed using the Lewis parabola which allows computation of the Lewis form factor.(1) The geometry factor is obtained from this Lewis factor and load sharing ratio. This method, which originally required graphical construction methods and more recently has been computerized, works reasonably well for external gears with thick rims.(2-6) However, when thin rims are encountered or when evaluating the strength of internal gears, the AGMA method cannot be used.

Consisting of only a ring gear b meshing with one or two planets a, a carrier H and an equal velocity mechanism V, a KHV gearing(Fig. 1) is compact in structure, small in size and capable of providing a large speed ratio. For a single stage, its speed ratio can reach up to 200, and its size is approximately 1/4 that of a conventional multi-stage gear box.

The south-pointing chariot exhibited at the Smithsonian Institution, Washington, D.C., (circa 2600 BC)is shown in Fig. 1. Although the mechanism is ancient, it is by no means either primitive or simplistic. The pin-tooth gears drive a complex system, wherein the monk on the top of the chariot continues to point in a preset direction, no matter what direction the vehicle in moved, without a slip of the wheels.(1)

Primitive gears were known and used well over 2,000 years ago, and gears have taken their place as one of the basic machine mechanisms; yet, our knowledge and understanding of gearing principles is by no means complete. We see the development of faster and more reliable gear quality assessment and new, more productive manufacture of gears in higher materials hardness states. We have also seen improvement in gear applications and design, lubricants, coolants, finishes and noise and vibration control. All these advances push development in the direction of smaller, more compact applications, better material utilization and improved quietness, smoothness of operation and gear life. At the same time, we try to improve manufacturing cost-effectiveness, making use of highly repetitive and efficient gear manufacturing methods.

The load carrying behavior of gears is strongly influenced by local stress concentrations in the tooth root and by Hertzian pressure peaks in the tooth flanks produced by geometric deviations associated with manufacturing, assembly and deformation processes. The dynamic effects within the mesh are essentially determined by the engagement shock, the parametric excitation and also by the deviant tooth geometry.

Involute Curve Fundamentals. Over the years many different curves have been considered for the profile of a gear tooth. Today nearly every gear tooth uses as involute profile. The involute curve may be described as the curve generated by the end of a string that is unwrapped from a cylinder. (See Fig. 1) The circumference of the cylinder is called the base circle.

The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.

The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.

The use of dimensionless factors to describe gear tooth geometry seems to have a strong appeal to gear engineers. The stress factors I and J, for instance, are well established in AGMA literature. The use of the rack shift coefficient "x" to describe nonstandard gear proportions is common in Europe, but is not as commonly used in the United States. When it is encountered in the European literature or in the operating manuals for imported machine tools, it can be a source of confusion to the American engineer.

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